Label noise and class imbalance are common challenges encountered in real-world datasets. Existing approaches for robust learning often focus on addressing either label noise or class imbalance individually, resulting in suboptimal performance when both biases are present. To bridge this gap, this work introduces a novel meta-learning-based dynamic loss that adapts the objective functions during the training process to effectively learn a classifier from long-tailed noisy data. Specifically, our dynamic loss consists of two components: a label corrector and a margin generator. The label corrector is responsible for correcting noisy labels, while the margin generator generates per-class classification margins by capturing the underlying data distribution and the learning state of the classifier. In addition, we employ a hierarchical sampling strategy that enriches a small amount of unbiased metadata with diverse and challenging samples. This enables the joint optimization of the two components in the dynamic loss through meta-learning, allowing the classifier to effectively adapt to clean and balanced test data. Extensive experiments conducted on multiple real-world and synthetic datasets with various types of data biases, including CIFAR-10/100, Animal-10N, ImageNet-LT, and Webvision, demonstrate that our method achieves state-of-the-art accuracy.